Let a- and b-2-k- then the point of intersection of the line r-a-b-a and r-b-a-b

We have nbsp;r×a=b×a ⇒ (r b)×a= 0 ⇒ (r b) is parallel to a ⇒ (r b)=λa ⇒ nbsp; r=b+ λa Similarly, the equation of the other line can be written as r=a+ μb Fo ...

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Standard XII

Mathematics

Dot Product

Let a=î+ĵ and...

Question

Let $\to a =^i +^j$ and $\to b = 2^i -^k$ then the point of intersection of the line $\to r \times \to a = \to b \times \to a$ and $\to r \times \to b = \to a \times \to b$

3^i +^j -^k

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3^i + 3^j -^k

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3^i +^j - 3^k

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3^i + 3^j + 3^k

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Solution

The correct option is A $3^i +^j -^k$
We have $\to r \times \to a = \to b \times \to a \Rightarrow (\to r - \to b) \times \to a = \to 0$
$\Rightarrow (\to r - \to b)$ is parallel to $\to a$
$\Rightarrow (\to r - \to b) = λ \to a$
$\Rightarrow \to r = \to b + λ \to a$
Similarly, the equation of the other line can be written as $\to r = \to a + μ \to b$
For the point of intersection of the above two lines, we have $\to b + λ \to a = \to a + μ \to b$
$\Rightarrow λ = μ = 1$
$∴$ The point of intersection is: $\to r = \to a + \to b = 3^i +^j -^k$

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Dot Product

Standard XII Mathematics

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Let →a=^i+^j and →b=2^i−^k then the point of intersection of the line →r×→a=→b×→a and →r×→b=→a×→b

Let $\to a =^i +^j$ and $\to b = 2^i -^k$ then the point of intersection of the line $\to r \times \to a = \to b \times \to a$ and $\to r \times \to b = \to a \times \to b$